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Roe B.P. — Probability and Statistics in Experimental Physics
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Название: Probability and Statistics in Experimental PhysicsАвтор: Roe B.P. Аннотация: This book is a practical introduction to the use of probability and statistics in experimental physics for graduate students and advanced undergraduates. It is intended as a practical guide, not as a comprehensive text in probability and statistics. The emphasis is on applications and understanding, on theorems and techniques that are actually used in experimental physics. Proofs of theorems are generally omitted unless they contribute to the intuition in understanding and applying the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to some of the Fortran routines available in the CERN library, but other systems, such as Maple, will also be useful. Topics covered include: basic concepts and definitions; general results, independent of specific distributions; discrete distributions; the normal distribution and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence limits; estimation methods; curve fitting, robustness estimates, and likelihood ratios; interpolating functions and unfolding problems; fitting data with constraints; robust estimation methods.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 208Добавлена в каталог: 18.10.2010Операции: Положить на полку |
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A postiori probability 3 4 a priori probability 1 3 103—105 Acceptance rejection method 65—67 73 Arrangements 28 37 Asymptotic efficiency of au estimate 121 123 Asymptotically normal distribution 123 163—166 171 B-spline functions 175 179 Background 13 26 31 70 112 143 157 159 176 Background subtraction 26 143 157 159 176 Bartlett S function 133 161 162 171 172 Bayes’ Theorem 102—104 113 Bernoulli trials 33 40 57 58 97 98 Betting odds for A against B 168 Biased estimate 132 Binomial coefficient 27 28 38 Binomial distribution (see Distributions binomial) Breit-Wigner distribution (see Distributions Breit-Wigner) Bridge hands of cards 28 30 38 Brownian motion 16 Bubble chamber 132 Buffon's needle 13 Cauchy distribution (see Distributions Breit-Wigner) Cdn toss 1 3 33 196 Central limit theorem 42 58 60 90 93 95 96 98 99 Central moment 7 13 25 CERN v 23 66 70 71 149 158 CERN library v Change of variable 18 21 171 184 Characteristic functions 54 58—63 81 85 86 Chi-square distribution (see Distributions chi-square) Chi-square fitting 119 12 125 127 128 139 143 147 149 151 152 154 157 159 173 180 Cofactor 83 155 Combinatorial 27 29 Combining probability estimates 128 Combining several measurements 21 23 25 131 198 Complete spline 174 composition 54 55 63 Compound probability 54 55 57 61 Computer program v 1 2 13 66 70 73 135 158 159 Computing v 13 62 66 68—70 91 99 117 129 135 154 158 159 178 179 183 188 198 Conditional probability 6 36 64 77 102 Confidence interval 102 105—107 110 111 Confidence level 105 109—111 Confidence limit 102 107 113 117 153 166 Constraints 119 125 138 180 183 188 Convergence in probability 120 Convolution 54 55 57 59—61 correlated 9 18 19 66 84 86 92 123 135 138 147 150 151 180—183 185 187—189 Correlation coefficient 9 17 18 20 75 83 89 126 Correlation matrix 82 183 Counting rate 25 26 Covariance 75 76 Covariance matrix 144 146 151 Covaxiance mapping 89 Crass section 39 Cubic B-splines 175—177 179 Cubic splines 173 178 Curve fitting 47 135 138 180 Dead time 13 Degrees of freedom 23 47 48 60 86—88 111 119 120 123 125 127 128 139 142 143 147 152 168 Density function 1 4 5 8 13 15 38 44 48 52 53 55 58 62 63 65 68—70 73 75 80 84 85 88 89 96 104 105 120 122 125 129 159 160 169 176 Dependence 8 18 21 180 Detector efficiency 176 Die 2—4 9 58 Differential probability function (see Density function) Diffusion 16 37 Direct probability 102 Discrete probability 5 6 29 33 Distribution function 1 3—5 38 49 60 62 63 69 94 95 128 161 171 189—191 Distributions, binomial distribution 33 35 37 39 40 42 45 53 57 58 60 97 101 110 111 117 196 Distributions, Breit — Wigner distribution 50 60 61 63 70 96 159 178 179 Distributions, Cauchy distribution (see Breit-Wigner distribution) Distributions, chi-square distribution 42 45 47 50 60 86 88 119 120 123 125 127 128 139 142 147 151 152 168 Distributions, exponential distribution 62 63 73 74 Distributions, F distribution 47 49 142 Distributions, gamma distribution 39 Distributions, gaussian distribution (see Distributions normal) Distributions, geometric distribution 57 58 Distributions, hypergeometric distribution 37 38 111 Distributions, Kolmogctrov — Smirnov Distribution 193 195 200 Distributions, multi-dimensional normal distribution 84 86 140 Distributions, multinomial distribution 37 Distributions, negative binomial distribution 37 Distributions, normal distribution 8 12 14 36 42 44—51 53 60 61 69 70 73—75 81 87 88 90—93 97 98 100 101 103 108 110 111 113 114 125 127 128 130 131 133 154 161 171 179 182 188 198 Distributions, Poisson distribution 33 35—40 42 45 55 57 58 60 70 91 100 105 109 111 117 128 130 Distributions, Rayleigh probability distribution 52 Distributions, runs distribution 187 188 Distributions, Smimov - Cramer-Von Mises distribution 191—193 Distributions, Student’s distribution 49 52 111 153 Distributions, two dimensional normal distribution 80 81 89 Dividing data in half 112 Drunkard’s Walk 16 Efficiency of an estimate 121 123 Efficiency of detector 72 73 Ellipse of concentration 80 Ellipsoid of concentration 83 85 Equations of constraint 180—182 184 Error estimate 16 23 25 49 52 53 105 114 138—141 151 156 157 164 184 Errors in quadrature 19 Excess (see Kurtosis) expectation value 6 7 25 76 133 136 137 163 164 184 Exponential distribution (see Distributions exponential) Extrapolated point 157 F distribution (see Distributions F) Factorials 27 29 30 Fair com 53 172 Feller, W. 3 Fisher’s lemma (see Lemma of Fisher) Fluctuations 89 90 Frequency function (see Density function) Gamma distribution (see Distributions gamma) Gamma function 51 Gaussian distribution (see Distributions normal) Generating functions 54 56 58 60 61 Geometric distribution (see Distributions geometric) HBOOK 70 71 158 Histogram package v 70 71 Histograms 45 70 72 73 177 179 189—191 196—198 Hypergeometric distribution (see Distributions Hypergeometric) Hypothesis of desperation 104 105 107 109 116 Hypothesis testing 47 169 171 190 193 196 198 Identical trials 2 Importance sampling 65 73 Independence 2 3 9 13 14 16—18 21—23 25 33 36 45 48 49 54 55 58 59 61 69 75 76 83 85—88 90 91 120 126—128 135 138 165 168 169 181 Integral probability (see Distribution function) Interpolated point 141 156 157 Interpolating functions 173—176 178 Inverse probability 102 113 Iterated logarithm 97 98 Iterations to find minima/maxima 149 159 183 184 188 Jacknife 161 171 James, F. 67 97 152 Khintchine, A. 97 Kolmogorov — Smirnov distribution (see Distributions Kolmogorov Kolmogorov — Smirnov test 193 Kroneker 87 kurtosis 7 8 153 154 166 Lagrange multipliers 180 Least squares 118 119 124 129 138 153 175 189 198 Lemma of Fisher 87 88 Likelihood contour 151—153 Likelihood ratio 161 168 171 Linear least squares 175 Linear regression 77 78 81 83 LOREN 72 73 Mann, M.B. and Whitney, D R 198 Maple V 158 Marbe, K. 3 Marginal probability 5 Maximum likelihood 118 120 139 151 158 159 162 Maximum likelihood, estimate 125 130 133 162 Mean 7 8 13 16 18 21—23 25 33 36—38 40 44 45 47 49 53 60 69 77 80 86—88 96 105 110 113 114 117 128 130 131 133 153 164 166 171 182 187 Measurement error 18 103 134 141 164 Median 8 method 120 123 129—133 135 159 160 Method, theorem 120 MINUIT 149 150 152 158 182 MODE 8 Modified chi-squared minimum, method 119 120 124 138 182 moment 7 13 47 50 57 61 75 Moment matrix 75 82 85—87 135 140 147 151 180 184 186 187 Monte Carlo efficiency 62 68 74 Monte Carlo simulation 62 70 74 97 129 158 172 177 178 Multi-dimensional distribution 75 82 Multi-dimensional normal distribution (see Distributions multi Multinomial coefficients 37 Multinomial distribution (see Distributions multinomial) Multiple correlation coefficient 84 Multiple scattering 14—16 21 22 25 43 76 79 82 93 96 99 134 169 Natural spline 173 174 Negative binomial distribution (see Distributions negative Non-linear parameters 135 147—149 154 Normal distribution (see Distributions normal) Not-a-knot condition 174 176 Parratt, L.G 104 Partial correlation coefficient 84 PCSAS v permutations 37 Pivotal quantity 111 Plural scattering 95 Poisson distribution (see Distributions Poisson) Poisson postulate 36 Poisson trials 58 Population mean 125 probability 1—3 Probability of causes 102 Propagation of errors 18 21 97 Pseudo-random number v 13 62—67 68 74 91 92 158 Quadratic form 76 77 Random number (see Pseudo-random number) Random walk 16 Randomization test 198 Randomness 1 2 RANMAR 66—68 Raudom variable 5—7 18 34 55 59 61 62 75 90 91 133 Rayleigh probability distribution (see Distributions Rayleigh) Regression analysis 118 138 Regression line 77 78 81 83 Regression plane 83 Regular estimate 121 Regularization method 145 177 Regularization parameter 145 Relative frequency 2 3 Renyi theorem 195 Resolution function 176 178 179 RMARIN 67 68 Robust 153 Root N law 14 21 runs 196 Runs distribution (see Distributions runs) Rutherford, scattering 16 93—96 Sagitta 163 164 Sample correlation coefficient 134 Sample mean 25 133 198 Sample space 5 13 18 Sampling 38 65 73 106 125 131 133 190 193 195 198 Sampling with replacement 32 37 Sampling without replacement 27 32 38 SAS v Semi-positive definite quadratic form 76 82 Significance level 191 Significance of a signal 111 143 146 178 191 Smirnov theorem 195 Spline functions 173 175 178 Standard deviation 7 8 18 33 61 80 97 99 103 105 111 112 151 152 171 Student’s distribution (see Distributions Student’s) Sufficient statistic 111 122 123 127 168 Sum of squares 86 119 Total correlation coefficient 83 Two dimensional distribution 75 Two dimensional normal distribution (see Distributions Two Unbiased estimate 121 Uncorrelated 9 76 85 89 Unfolding 173 176 178 179 Unphysical region 117 Variance 7 8 10 12 18—26 34 36 44 45 47 49 51—53 57 59 60 69 78 80 86—88 90 95 96 99 100 103 105 110 113 114 120 121 123 125 127 130 135 137 139 141—144 151 153 156 164—166 169—171 177 182 187 191 198 von Neumann, J. 65 Wang's theorem 195 Weighted mean 114 128 Weights 24 65 96 114 119 128 138 143—145 177 Wilcoxon, F. 198 Yost, G.P. 63 97
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